$$ \text{Find } 2011^2 - 2010^2 \text{?} $$

Question

UpStudy AI · Accepted Answer

To find the value of $$ 2011^2 - 2010^2 $$, we can use the **difference of squares** formula:

$$
a^2 - b^2 = (a - b)(a + b)
$$

**Let's apply this formula:**

1. **Identify $$ a $$ and $$ b $$:**
   $$
   a = 2011 \
   b = 2010
   $$

2. **Apply the difference of squares formula:**
   $$
   2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
   $$

3. **Calculate the differences and sums:**
   $$
   2011 - 2010 = 1 \
   2011 + 2010 = 4021
   $$

4. **Multiply the results:**
   $$
   (1)(4021) = 4021
   $$

**Therefore,**
$$
2011^2 - 2010^2 = 4021
$$
$$ 2011^2 - 2010^2 = 4021 $$

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